Kerry Back
A call option on a futures contract gives you the right to acquire a long position in the futures (buy the futures) at the option strike.
A put option gives you the right to acquire a short position in the futures (sell the futures) at the option strike.
If you’ve sold an option and it is exercised, you are rolled into the opposite futures position.
On the exercise date of a call, daily settlement produces a cash flow of futures_settlement_price - strike to the party who exercised and the opposite cash flow to the party who sold the call.
For a put, it is strike - futures_settlement_price.
Everyone who wants could unwind the futures position by making an offsetting trade on the day of exercise.
\[C = \frac{p \times \text{\$}5 + (1-p)\times \text{\$}0}{1.05}\]
\[\text{\$}100 = \frac{p \times \text{\$}110 + (1-p) \times \text{\$}90}{1.05}\]
\[\text{\$}100 = p \times \text{\$}110 + (1-p) \times \text{\$}90\]
\[\frac{1 - e^{-\sigma \Delta t}}{e^{\sigma \Delta t} - e^{-\sigma \Delta t}}\]